Jak 1 is a better Crash Twinsanity than Crash Twinsanity in regards to the open areas. It is not an open world tho, since the worlds are basically hubs from which you access the 'levels' separated by long lava canyons (corridors). Although Daxter features in the title, he is not playable. The story is as basic as you can get.

Jak II is fascinated by many games. It loves Ratchet and Clank, GTA, Tony Hawks, Wipeout, Whack-a-mole. It seems it doesn't want to be a platformer that much, although some levels and sections that recall the og's gameplay are present. The story is more prominent but also a bit confusing.

Jak 3 takes its own identity crisis to the next level, to the point where the number of sections in which you are not platforming far surpass the ones in which you are. The story also took a big nosedive.

I like how the first game is Light, the second is Darkness and the third is Balance (the Tao appears in the hud). Overall the games are worth playing, especially the 1st and the 2nd.

I would have loved to see how to series would have continued, had Naughty Dog not ripped off GTA (making it better). Truly, the 2nd and 3rd games feel like spinoffs to the first, and I kinda dig that quite a bit.